Lattice field theory simulations of graphene

Abstract

We discuss the Monte Carlo method of simulating lattice field theories as a means of studying the low-energy effective theory of graphene. We also report on simulational results obtained using the Metropolis and Hybrid Monte Carlo methods for the chiral condensate, which is the order parameter for the semimetal-insulator transition in graphene, induced by the Coulomb interaction between the massless electronic quasiparticles. The critical coupling and the associated exponents of this transition are determined by means of the logarithmic derivative of the chiral condensate and an equation-of-state analysis. A thorough discussion of finite-size effects is given, along with several tests of our calculational framework. These results strengthen the case for an insulating phase in suspended graphene, and indicate that the semimetal-insulator transition is likely to be of second order, though exhibiting neither classical critical exponents, nor the predicted phenomenon of Miransky scaling.

Effect of Coulomb interactions on the physical observables of graphene

“…The influence of the substrate in this context has also been analyzed in [53]. Monte Carlo calculations in a lattice gauge theory framework predict the opening of a gap [31,54]. A gap has also been claimed in very recent angle-resolved photoemission spectroscopy (ARPES) measurements of epitaxial graphene upon dosing with small amounts of atomic hydrogen [55].…”

“…N is the number of fermionic species in the problem, which in the case of graphene with the spin and valley degeneracies is N = 4. This procedure was followed in the early publications [28,29] and was later reconsidered in [30][31][32].…”

Artificial honeycomb lattices for electrons, atoms and photons

“…In recent years, several efforts have been made [98][99][100][101] to describe electrons moving in a honeycomb lattice and interacting through the non-relativistic Coulomb force. In this case the strength of interactions is measured by the dimensionless parameter [5,12] α ee ≡ e 2 /( hv F ), where e is the absolute value of the electron's charge, is a suitably-defined dielectric constant, and v F is the Fermi velocity.…”

“…A excitonic insulating phase has been predicted to occur spontaneously [99][100][101] at a critical value of the Coulomb coupling constant α ee 1.1 for N f = 4 fermion flavors. Note that electrons in natural suspended graphene are characterized by α ee ∼ 2.2 (since, in this case, ∼ 1 and v F ∼ 10 6 m/s).…”

Interplay between sublattice and spin symmetry breaking in graphene

“…Sublattice symmetry breaking in graphene could arise spontaneously, due to some electronic phase transition, [5][6][7][8][9] or due to the coupling of graphene to some substrate, like silicon carbide 10,11 and boron nitride. [12][13][14] Sublattice symmetry breaking would make it energetically favorable for the electrons to stay in one of the sublattices, resulting in pseudospin order 15 (either spontaneous, or induced).…”